# Elastic Moduli - Young’s Modulus

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Elastic Modulus

• Elastic modulus is the ratio of stress and strain.

• Elastic modulus is a characteristic value of each material. This means gold will have a specific value of elastic modulus and rubber will have a specific value of elastic modulus etc.

• "k"="Stress"/"Strain" Where k= Elastic modulus.

Types of elastic modulus:

1. Young’s Modulus:

Young’s modulus is derived from the name of the scientist who defined it.

• It is the ratio of longitudinal stress to longitudinal strain.

• It is denoted by Y.

• Mathematically:

• "Y"= "longitudinal stress"/ "longitudinal strain" = σ/ ε

• = ("F"/"A")/((Δ"L")/"L")

• "Y"="FL"/(Δ"L")

• If Young’s modulus is more, to produce a small change in length more force required.

• S.I. unit is "Nm"^(–2) or Pascal (Pa).

• Metals have comparatively greater Young’s Modulus. To change the length of metals, greater force is required.

Young’s Modulus: Application

• In industrial construction, steel is preferred over copper. The reason behind this is steel is more elastic than copper.

• If there is slight deformation in steel due to contraction and expansion it will come back to its original position.

• Steel is preferred over copper to construct bridges.

 Substance Density rho ("kgm"^-3) Youngs modulus Y (10^9"Nm"^-2) Ultimate strength, sigma_u(10^6"Nm"^-2) Yield strength sigma_y(10^6"Nm"^-2) Aluminum 2710 70 110 95 Copper 8890 110 400 200 Iron (wrought) 7800-7900 190 330 170 Steel 7860 200 400 250 Glass 2190 65 50 - Concrete 2320 30 40 - Wood 525 13 50 - Bone 1900 9.4 170 - Polystyrene 1050 3 48 -
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